报告题目:Elliptic curves, continued fractions and Somos recurrences

报告人：常向科 教授 (中国科学院数学与系统科学研究院)

报告时间：2024.04.22 15:00-16:00

报告地点：广B208

摘要: Somos-4 and Somos-5 are bilinear recurrence relations that can be obtained as reductions of the discrete KP equation. They exhibit interesting integrality, behind which it is the Laurent phenomenon appearing as a key property of cluster variables in Fomin and Zelevinsky’s cluster algebras. This talk is devoted to presenting how to derive explicit solutions of Somos-4 and Somos-5 in terms of Hankel determinants based on elliptic curves and continued fractions, which is mainly based on Hone’s works as well as our recent results.

报告人简介：常向科，中国科学院数学与系统科学研究院副研究员，博士生导师，主要从事可积系统及相关领域的交叉研究， 部分研究成果发表在《Adv. Math.》、《Commun. Math. Phys.》、《Int. Math. Res. Not.》、《J. Differ. Equations》、《J. Nonlinear Sci.》、《Nonlinearity》、《Numer. Math.》、《Sci. China Inform. Sci.》、《Sci. China Math.》、《SIAM J. Discrete Math.》、《Stud. Appl. Math.》等国内外重要学术刊物上，研究工作得到国家自然科学基金委优秀青年科学基金的资助。曾获得中科院优秀博士学位论文奖、中科院院长奖，入选中科院青年创新促进会会员、中科院数学院“陈景润未来之星”计划等，并担任《Physica D》杂志青年编委、中科院青促会数理分会会长等。

邀请人：沈守枫